The rules of Jigsaw Killer Sudoku are based upon those of Jigsaw Sudoku and Killer Sudoku, both of which build on Sudoku itself. In all of these puzzles you must place each of the numbers 1 to 9 (or 1 to whatever the width of the puzzle is) into all of the rows, columns and bold-lined regions. In the case of Jigsaw versions, these bold-lined regions are irregular shapes, replacing the 3x3 boxes of standard Sudoku or Killer Sudoku.

In both Jigsaw and regular Killer Sudoku, you must also place the numbers so that each dashed-line 'cage' adds up to the total given at the top-left in smaller digits. For example, the three-square '7' cage at the very top-left of the puzzle below must add up to 7. You also cannot repeat a number within a cage, so this means for example that the solution to '7' must be 1 and 2 and 4, not 1+3+3 or 2+2+3 or any other possible solution (although in this case these would in fact be disallowed by the standard rules of Sudoku anyway since they are all in a single region).

By marking some of the 'only fit' numbers in as pencilmarks, we can start to solve the puzzle.

In the first column we can place 6, 8 and 9 in the '23' region as the only valid solution to this cage. We already know that the 7 cage at the top-left can only contain 1, 2 and 4. This means that are only two remaining cages in this first column where the '3' can fit - the one where it is marked in below, and the '16' cage beneath it. However, none of the solutions to the 16 cage can contain a 3 without also using a 6, 8 or 9 - and thus are all invalid because 6, 8 and 9 have already been used in this column. So the '3' must go where marked:

Notice how in this picture that above the puzzle the list of fits for the '16' region is shown, by using the 'Show current clue fits' solving aid (ticked to the right of the puzzle). This can be very helpful, particularly when first solving these puzzles.

Looking further at the possible fits for the '16' cage, we can see that the only solution given the numbers we have already placed in other cages is 4, 5 and 7. This means we can eliminate the '4' from the top two squares of the first column. But we already know there must be a 4 in that '7' cage, so we can place it in the remaining square:

Once the puzzle is fully-solved you will have 1 to 9 in each row, column and jigsaw shape, and each cage will add up to the total at the top-left:

Once you get really good at Jigsaw Killer Sudoku, you might even find you can solve many of them faster than regular Jigsaw Sudoku!